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Vertically stretch by a factor of 3, then translate the equation 2 units up

F(x)=3x+1 arrow symbol

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To transform the function \( F(x) = 3x + 1 \) by applying a vertical stretch by a factor of 3 and then translating it 2 units up, we can follow these steps:

  1. Vertical Stretch: To stretch a function vertically by a factor of \( k \), we multiply the entire function by \( k \). In this case, \( k = 3 \).

    \[ F(x) = 3(3x + 1) = 9x + 3 \]

  2. Translate Up: To translate the function up by \( d \) units, we add \( d \) to the entire function. Here, \( d = 2 \).

    \[ F(x) = 9x + 3 + 2 = 9x + 5 \]

Thus, the final transformed function after applying both transformations is:

\[ F(x) = 9x + 5 \]